When the metallic bar is heated and its expansion is prevented, thermal stress is developed in it. The thermal strain is given by $\epsilon = \alpha \Delta T$. According to Hooke's law, Young's modulus $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F / A}{\alpha \Delta T}$. Therefore, the compressive force developed is $F = Y A \alpha \Delta T$. Given values: $Y = 0.5 \times 10^{11}\text{ N m}^{-2}$ $A = 10^{-3}\text{ m}^2$ $\alpha = 10^{-5}\ ^\circ\text{C}^{-1}$ $\Delta T = 100^\circ\text{C} - 0^\circ\text{C} = 100^\circ\text{C}$ Substituting the values into the formula: $F = (0.5 \times 10^{11}) \times (10^{-3}) \times (10^{-5}) \times (100)$ $F = 0.5 \times 10^{(11 - 3 - 5 + 2)}$ $F = 0.5 \times 10^5\text{ N}$ $F = 50 \times 10^3\text{ N}$